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  title = {Study on the loss of information caused by the "positivation" of graph kernels for 3D shapes},
  author = {Loosli, Gaëlle},
  booktitle = {24th European Symposium on Artificial Neural Networks Bruges, Belgium, April 27-28-29},
  year = {2016},
  abstract = {In the presented experimental study, we compare the classification power of two variations of the same graph kernel. One variation is designed to produce semi-definite positive kernel matrices ($K_{matching}$) and is an approximation of  the other one, which is indefinite ($K_{max}$). 
  We show that using adaptated tools to deal with indefiniteness (KSVM), the original indefinite kernel outperforms its positive definite approximate version. 
  We also propose a slight improvement of the KSVM method, which produces non sparse solutions, by adding a fast post-processing step that gives a sparser solution.}
  author = {Gaëlle Loosli and Stéphane Canu and Cheng Soon Ong},
  title = {Learning {SVM} in Kre{\u{i}}n Spaces},
  journal = {{IEEE} Trans. Pattern Anal. Mach. Intell.},
  volume = {38},
  number = {6},
  pages = {1204--1216},
  year = {2016},
  url = {https://doi.org/10.1109/TPAMI.2015.2477830},
  doi = {10.1109/TPAMI.2015.2477830},
  abstract = {This paper presents a theoretical foundation for an SVM solver in
	Kre\u{i}n  spaces. Up to now, all methods are based either on the matrix
	correction, or on non-convex minimization, or on feature-space
	embedding. Here we justify and evaluate a solution that uses the
	original (indefinite) similarity measure, in the original Kre\u{i}n 
	space. This solution is the result of a stabilization procedure. We
	establish the correspondence between the stabilization problem (which
	has to be solved) and a classical SVM based on minimization (which is
	easy to solve). We provide simple equations to go from one to the
	other (in both directions). This link between stabilization and
	minimization problems is the key to obtain a solution in the original
	Kre\u{i}n  space. Using KSVM, one can solve SVM with usually troublesome
	kernels (large negative eigenvalues or large numbers of negative
	eigenvalues). We show experiments showing that our algorithm KSVM
	outperforms all previously proposed approaches to deal with indefinite
	matrices in SVM-like kernel methods.}